MathDB

For a positive integer

n

, define

f(x)

to be the smallest positive integer

x

satisfying the following conditions: there exists a positive integer

k

and

k

distinct positive integers

n=a_0<a_1<a_2<\cdots<a_{k-1}=x

such that

a_0a_1\cdots a_{k-1}

is a perfect square. Find the smallest real number

c

such that there exists a positive integer

N

such that for all

n>N

we have

f(n)\leq cn

.
Proposed by Fysty and amano_hina

Problem Statement